Nuclear Physics A 813 (2008) 199–211
www.elsevier.com/locate/nuclphysa
Neutron decay spectroscopy of neutron-rich
oxygen isotopes
N. Frank a,b,c,∗,1 , T. Baumann b , D. Bazin b , B.A. Brown a,b , J. Brown d ,
P.A. DeYoung e , J.E. Finck f , A. Gade a,b , J. Hinnefeld g , R. Howes h ,
J.-L. Lecouey b,2 , B. Luther c , W.A. Peters a,b,3 , H. Scheit b,4 , A. Schiller b ,
M. Thoennessen a,b , J. Tostevin i
a Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
b National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA
c Department of Physics, Concordia College, Moorhead, MN 56562, USA
d Department of Physics, Wabash College, Crawfordsville, IN 47933, USA
e Department of Physics, Hope College, Holland, MI 49423, USA
f Department of Physics, Central Michigan University, Mt. Pleasant, MI 48859, USA
g Department of Physics and Astronomy, Indiana University at South Bend, South Bend, IN 46634, USA
h Department of Physics, Marquette University, Milwaukee, WI 53201, USA
i Department of Physics, Faculty of Engineering and Physical Sciences, University of Surrey,
Guildford, Surrey GU2 7XH, United Kingdom
Received 13 August 2008; received in revised form 4 September 2008; accepted 9 September 2008
Available online 18 September 2008
Abstract
Neutron decay spectroscopy of neutron-rich oxygen isotopes has been performed using the two-proton
knock-out reaction 9 Be(26 Ne, X)24,23,22 O. A combination of the knock-out of valence and core protons
can explain the three observed spectra. These knock-out processes are selective and preferentially populate
hole states. The observed narrow resonance state in 23 O at an excitation energy of 2.8(1) MeV was assigned
to the 5/2+ state.
* Corresponding author.
E-mail address: [email protected] (N. Frank).
1 Present address: Physics Department, Illinois Wesleyan University, Bloomington, IL 61701, USA.
2 Present address: Laboratoire de Physique Corpusculaire, IN2P3, 14050 Caen, France.
3 Present address: Department of Physics and Astronomy, Rutgers, The State University of New Jersey, Piscataway,
NJ 08854, USA.
4 Present address: Nishina Center for Accelerator Based Science, RIKEN, Wako, Saitama 351-0198, Japan.
0375-9474/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.nuclphysa.2008.09.009
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N. Frank et al. / Nuclear Physics A 813 (2008) 199–211
© 2008 Elsevier B.V. All rights reserved.
PACS: 21.10.Pc; 23.90.+w; 25.60.Gc; 29.30.Hs
Keywords: N UCLEAR REACTIONS 9 Be(26 Ne, X)22,23,24 O, E = 86 MeV/nucleon; measured fragment and neutron
energy- and angular-spectra, (fragment)(neutron)-coin, neutron decay energy spectra; deduced reaction mechanism
features. 23 O observed unbound state
1. Introduction
It has been established that in nuclei far from stability the traditional shell ordering can change,
where some energy gaps between orbitals decrease or even disappear [1,2] and others appear or
widen [3]. Current shell model calculations suggest large gaps at N = 14 and 16 for 22 O and
24 O, respectively [4]. These shell gaps result from the shifted energies of the 0d
5/2 , 1s1/2 and
0d3/2 orbitals of neutrons in oxygen isotopes near the drip line. The spin–isospin component of
the nucleon–nucleon force has been suggested as the reason for this change in structure [5,6]
resulting in an additional attraction between protons and neutrons of the same orbital angular
momentum (l) and opposite spin, i.e., j> = l + 1/2 and j< = l − 1/2. Thus the overlap of wave
functions for a neutron in the 0d3/2 orbital and a proton in the 0d5/2 orbital results in increased
binding [7]. This could explain why the addition of one proton in the 0d5/2 orbital results in 26 F
being bound while 25 O is unbound.
The first experimental evidence for a widening of the N = 16 shell gap near the neutron drip
line was found in one-neutron separation-energy systematics [8]. To quantify this energy gap for
N = 16 between the 0d3/2 and 1s1/2 orbitals, a search for bound excited states in 23,24 O was
performed [9]. The lack of bound excited states provided further evidence for a large shell gap
in 23,24 O and the 3/2+ particle state of 23 O was observed in the 2 H(22 O,23 O)1 H reaction at an
excitation energy of 4 MeV [10]. The recent measurement of the neutron unbound ground state of
25 O deduced an energy gap for the 1s
1/2 and the 0d3/2 orbitals to be 4.86(13) MeV, establishing
the N = 16 gap [11]. The first evidence of the N = 14 gap was deduced from the high excitation
energy of the first 2+ state in 22 O [12].
In the present work, a search for unbound excited states in the neutron-rich oxygen isotopes
22,23,24 O was performed using a two-proton knock-out reaction from 26 Ne. The first observation
of a narrow resonance in 23 O has already been reported [13]. Two-proton knockout reactions with
beams of intermediate-energy heavy-ions have been successfully used to explore the structure of
neutron-rich nuclei [14,15]. The experimental evidence that these reactions are direct means they
yield structure information about the populated states.
2. Experimental setup
The experiment was performed at the National Superconducting Cyclotron Laboratory
(NSCL) at Michigan State University. The primary beam of 140 MeV/u 40 Ar impinged on a
893 mg/cm2 Be production target. The average beam intensity was 105 pnA. The fragments of
interest were separated by the A1900 fragment separator [16]. An achromatic 750 mg/cm2 thick
acrylic wedge degrader was placed at the dispersive intermediate image of the A1900 to achieve
isotopic separation of the secondary 26 Ne beam. Some neutron–fragment coincidence data were
recorded with the momentum slits at the intermediate image set an acceptance of 1% and some
with an acceptance of 3%. The 26 Ne beam energy at the end of the A1900 was 86 MeV/u.
N. Frank et al. / Nuclear Physics A 813 (2008) 199–211
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Fig. 1. 26 Ne beam selection plot from the A1900 fragment separator. The vertical lines in the plot indicate the location
of the horizontal slits at the final focal plane of the fragment separator.
Fig. 2. The MoNA/Sweeper experimental setup [17,18].
Fig. 1 shows the composition and corresponding positions of secondary beam particles at the
A1900 focal plane. The main contaminants, 27 Na and 29 Mg, were reduced by ±10 mm slits at
the focal plane as indicated by the vertical lines in Fig. 1. A 26 Ne beam purity of about 93%
was achieved with a particle rate of about 7000/s. A plastic scintillator at the end of the A1900
provided an event-by-event start time of the secondary beam particles.
The secondary beam entered the experimental setup shown in Fig. 2. Trajectories of incoming
secondary beam particles were measured using two 15 × 15 cm2 position-sensitive parallel plate
avalanche counters (PPACs) with a pad pitch of 1.27 mm. A quadrupole triplet downstream from
the PPACs focused the beam onto the reaction target. The resolution of the position measurement
at the target was 2.4 mm (note, all resolutions are quoted in terms of Full Width at Half Maximum
(FWHM)). A 0.254 mm thick scintillator was placed directly in front of the 721 mg/cm2 thick Be
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reaction target to determine the time-of-flight of the secondary beam. The distance between this
target scintillator and the A1900 timing scintillator was 35.7 m. The neutron-unbound isotopes
of interest produced in the reaction target immediately decayed into a charged fragment and a
neutron. Due to the high velocity of the incoming secondary beam the charged fragments and the
neutrons were strongly forward focused. A large-gap sweeper magnet bent the charged fragments
away from the neutrons which were detected at zero degrees.
The superconducting 4 Tm sweeper magnet has a vertical gap of 14 cm and a bending angle
of 43◦ [19]. It was designed and constructed at the National High Magnetic Field Laboratory
at Florida State University. For the neutron–fragment coincidence data the magnetic field was
set to 3.5232 Tm. A suite of detectors behind the sweeper magnet measured particle trajectories
and provided particle identification. Two 30 × 30 cm2 position sensitive cathode-readout drift
chambers (CRDCs), separated by 1.87 m, allowed the fragment position and direction to be
measured. The resolution of the extracted angles was 2.4 mrad. Energy losses in a 65 cm long
ion chamber (EIC ) and a 40 × 40 cm2 , 4.5 mm thin (ESc ) plastic scintillator provided the
separation and identification of elements. The IC pulse-height signal was corrected for the drift
time within the detector volume. The particles stopped in a 15 cm thick plastic scintillator where
the remaining kinetic energy (RKE) was measured. The pulse-heights of the thin and the thick
scintillators were corrected for position dependence in both the dispersive and non-dispersive
directions.
Neutrons were detected in the Modular Neutron Array (MoNA) [20,21] placed at a distance
of 8.2 m from the reaction target. MoNA consists of 9 × 16 stacked 2 m long plastic scintillator
bars with photomultiplier tubes (PMT) on both ends. Horizontal position and neutron time-offlight (ToF) are determined from the time difference and the mean time, respectively, of the two
PMT signals with resolutions of ∼ 12 cm and ∼ 0.24 ns. The detectors are shadowed vertically
by the gap of the sweeper magnet and horizontally by an opening in the shielding wall in front
of MoNA shown in Fig. 2. The horizontal opening shields many neutrons near the edges of
the detector bars. The allowed straight-line paths from the target through the openings translate
into an opening angle of ±3.17◦ in the vertical direction and −6.45◦ to 4.64◦ in the horizontal
direction.
3. Data analysis
The decay energy spectra for 22,23,24 O∗ were calculated by the invariant mass method using
the relativistic four-momentum vectors of the neutron and 21,22,23 O in the lab frame. This required
the determination of the angles and energies of the neutrons and the fragments. However, first
it was necessary to cleanly identify the 26 Ne secondary beam and the produced fragments. The
26 Ne beam particles were separated event-by-event by the difference in ToF between the A1900
timing scintillator and the target scintillator as shown in Fig. 3.
The fragments recorded in the charged particle detectors behind the sweeper magnet were
separated first by element and then by isotope. The left side of Fig. 4 shows the energy loss as
measured by the IC versus the energy loss in the thin scintillator. Nitrogen, oxygen, fluorine as
well as scattered neon can be clearly identified and the oxygen isotopes were selected with the
two-dimensional gate shown in left panel of Fig. 4. The oxygen isotopes were then separated
by gating on the RKE versus an adjusted ToF spectrum as shown in the middle panel of Fig. 4.
This adjusted ToF was calculated from the timing between the thin scintillator and the target
scintillator. It was corrected for energy spread and path length differences through the magnet
and in the thin scintillator.
N. Frank et al. / Nuclear Physics A 813 (2008) 199–211
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Fig. 3. Time-of-flight (ToF) between the A1900 timing scintillator and the scintillator in front of the reaction target.
Fig. 4. Energy loss in the ionization chamber EIC versus energy loss in the thin scintillator ESc (left), RKE scintillator
energy versus adjusted ToF (middle), and the projection taken along the solid line on the RKE versus adjusted ToF plot
where the solid curves represent Gaussian fits of the 21,22,23 O isotopes (right). The parallelogram on the RKE versus
adjusted ToF plot shows the accepted events along the projection line.
The right panel of Fig. 4 shows the final isotope separation produced by taking a straight
line projection through the isotopes. The solid lines are for fits with three Gaussian distributions
for 21,22,23 O. The experimental setup required a fragment–neutron coincidence that prevented
observation of 24 O.
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Fig. 5. Angles (left) and energies (right) at the reaction target for 21 O (top), 22 O (middle) and 23 O (bottom) isotopes in
coincidence with neutrons. The smooth lines are results of simulations described in Section 4.
The energy and the angle of the fragments at the target position were reconstructed from the
trajectories following the magnet. This was achieved with a method that takes into account the
measured position at the target in the dispersive direction [22]. The ion-optical transformation
matrix was produced using COSY INFINITY [23] based on measured magnetic field maps.
The angle and energy resolution of the fragments as emitted from the target was 6.4 mrad and
0.9 MeV/u, respectively. Fig. 5 shows the fragment angular distribution (left) and the fragment
kinetic energies (right) for 21,22,23 O fragments. The kinetic energy is a sum of the reconstructed
energy and the average energy loss of the fragment through half of the reaction target. The peak of
the angular distributions increases with decreasing mass of the fragment which is consistent with
a direct production mechanism or with an increasing number of emitted particles. The kinetic
energies decrease with increasing mass because of the acceptance of the sweeper magnet which
cuts off fragments with lower momentum, especially for 21 O. The large width of kinetic energies
of the 23 O fragments could be due to contaminations from the much more strongly populated
22 O which could not be completely separated as shown in Fig. 4. The smooth lines in this and
the following two figures are the results of simulations which are described in more detail in
Section 4.
N. Frank et al. / Nuclear Physics A 813 (2008) 199–211
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Fig. 6. Horizontal (left) and vertical (right) positions of neutrons in coincidence with 21 O (top), 22 O (middle) and 23 O
(bottom) isotopes. The smooth curves are results of simulations described in Section 4.
Neutrons were detected with MoNA in coincidence with the 21,22,23 O fragments. The kinetic
energy of the neutrons was calculated from the ToF between the target scintillator and the time
measured by MoNA. A cut was applied to eliminate γ rays from reactions in the target [24].
The positions in the horizontal and vertical directions of the earliest neutron signal in coincidence with each of the three oxygen isotopes are shown in Fig. 6. While in the horizontal
direction neutrons within the acceptance are observed along the full width of MoNA (2 m), the
limited vertical acceptance results in only about 1 m being illuminated vertically. This is consistent with the shadowing of MoNA due to the vertical gap of the sweeper magnet. The sharp
peak visible for neutrons in coincidence with 22 O is already a first indication for the emission
of low-energy neutrons in the center-of-mass frame of 23 O. In contrast, neutrons in coincidence
with 21 O show a completely flat distribution, while there is some evidence for a broader peak for
23 O coincidence data. Again, this peak could be due to contaminations from 22 O which could
not be completely separated as shown in Fig. 4.
The azimuthal angles of the neutrons were derived from the interaction point in MoNA relative
to the beam axis. The angle and energy resolutions as calculated from the measured parameters
were 19 mrad and 3.8 MeV, FWHM, respectively. Fig. 7 shows the angles and the kinetic energy
distributions for neutrons in coincidences with 21,22,23 O fragments. The sharp peaks in the angle
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Fig. 7. Neutron angles (left) and energies (right) at the reaction target in coincidence with 21 O (top), 22 O (middle) and
23 O (bottom) isotopes. The smooth lines are the results of simulations described in Section 4.
spectra, especially at small angles, are due to the fact that the vertical position is known only in
increments of 10 cm from the vertical position of the bar. The neutron angular distributions and
the energy spectra support the observations from the position spectra. Neutrons in coincidence
with 22 O show a narrow energy peak and small angles indicating small decay energies in 23 O.
The contributions at small angles in the neutron spectra in coincidence with 23 O may result from
the 22 O contamination in the data. As in the previous two figures the smooth curves are results
from simulation which will be described in Section 4.
Monte Carlo simulations that include the geometric acceptances, intrinsic efficiencies and
resolutions of all detectors were performed in order to extract the properties of the excited states
from the data. The reaction mechanism was described by a Glauber reaction model [25]. Angular
straggling and energy loss in the target were also included.
The unbound resonances were included in the simulations in the form of a Breit–Wigner
distribution parameterized by a resonance energy (Er ) and width (Γ ) [26]. In addition, a nonresonant
√ −E/Tbackground distribution was simulated by a Maxwellian or thermal distribution F (E) ∼
Ee
where the temperature T (in MeV) was a free parameter [27].
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Fig. 8. Decay energy spectra of 22,23,24 O∗ (data points). The smooth curves are results from simulations; see text for
details.
4. Results and discussion
The decay energy spectra for the decay of 22,23,24 O to 21,22,23 O, respectively, are shown in
Fig. 8. While the 22 O and 24 O data show a broad distribution, the spectrum for 23 O peaks sharply
at very low decay energies.
The 22 O (top) can be described with a non-resonant background simulated by a thermal distribution with a temperature of 1.6 MeV. The 23 O spectrum (middle) was fit with the sum (solid)
of a low-lying resonance of 45(2) keV (dash-dotted) and a thermal distribution of temperature
0.95 MeV (dashed). The apparent observed (100 keV) width of the narrow peak is due to the
experimental resolution and only an upper limit of 30 keV for the width can be extracted from
the data. The statistics for the 24 O spectrum (bottom) are low and, as indicated already by the
neutron position and angle spectra, these data could be contaminated by a non-resolved contribution from the much more strongly populated 23 O. The data could be reasonably described with a
resonance at 700 keV and a width of 100 keV (dash), a non-resonant background with a temperature of 1.5 MeV (dotted) in 24 O in addition to the 23 O contamination (dash-dotted). Although
such a resonance is consistent with the data, the spectrum could also be described with a sum
(solid) of the 23 O background (dot-dashed) and a non-resonant background (dotted) simulated by
a temperature of 2 MeV, shown in Fig. 9. The result of these simulations, which describe the three
decay-energy spectra well, also reproduce the individual fragment angles and energies (Fig. 5),
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Fig. 9. Decay energy spectrum of 24 O. The thin smooth line corresponds to a sum of simulations of 23 O contaminations
(dot-dashed) and a non-resonant background in 24 O with a temperature of 2 MeV (dotted).
neutron x- and y-positions (Fig. 6), and, neutron angles and energies (Fig. 7). The individual
contributions shown in these figures for 23 O and 24 O are the same as in Fig. 8.
The observed decay energy spectra for all three isotopes can be explained within a direct reaction description of the two-proton knockout from 26 Ne. The dominant shell-model configuration
of the 26 Ne ground state is two sd-shell protons coupled to a 24 O core [28]. Thus, the two-proton
knockout [29] from 26 Ne can proceed by removal of two protons from the sd-shell, one proton
from the sd-shell and one from the p-shell, or two protons from the p-shell. These would result
in 24 O configurations of π(0p1/2,3/2 )6 , π(0p1/2,3/2 )−1 π(0d5/2 )1 , and π(0p1/2,3/2 )−2 π(0d5/2 )2 ,
respectively.
The most obvious direct reaction is the removal of the two protons in the sd-shell. This leads
predominantly to the ground-state of 24 O which is particle stable and does not decay by the
emission of a neutron. With the full sd-shell model wave function [30,31], the cross section
to the 2+ state of 24 O is over a factor of ten smaller than that for populating the ground state.
Such a small contribution is consistent with the low statistics observed for 24 O and the tentative
observation of a resonance state at about 700 keV shown in the bottom panel of Fig. 8. This
would correspond to an excitation energy of about 4.8 MeV in 24 O assuming the neutron decays
to the ground state of 23 O. This assumption is justified because 23 O does not have any bound
excited states [9]. However, this assignment is only tentative because the spectrum could also be
described without a contribution from a resonance in 24 O as shown in Fig. 9.
The knockout of one proton from the sd-shell and one from the p-shell, resulting in a 24 O configuration of π(0p1/2,3/2 )−1 π(0d5/2 )1 , is a more complicated situation. This proton configuration has negative parity and so will mix with neutron excitations of the form ν(0p)−1 × ν(0d3/2 )1
(case a), ν(0d5/2 )−1 × ν(0f 1p)1 (case b), and ν(1s1/2 )−1 × ν(0f 1p)1 (case c). Fig. 10 shows
the possible admixtures of the proton excitation (π ) with the neutron excitations (ν). The first
two cases (a, b) would emit a high-energy neutron leading to the 5/2+ and 1/2+ states in 23 O, respectively [32]. The efficiency of the current setup for detection of these high-energy neutrons is
very small. The 1/2+ state corresponds to the ground state of 23 O which does not emit neutrons.
This leaves the first excited 5/2+ state which we assign to the observed low-energy peak shown
in the middle panel of Fig. 8. The last case (c) has a large spectroscopic overlap with high-lying
negative-parity excitations in 23 O and most probably decays by the emission of two or more neutrons, thus contributing to the non-resonant background in coincidence with 21 O shown in the
top panel of Fig. 8.
N. Frank et al. / Nuclear Physics A 813 (2008) 199–211
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Fig. 10. Admixtures of proton and neutron excitations. The left side shows the knockout of the core (p-shell) proton. The
neutron level diagrams on the right show three possible scenarios for cross shell excitations; see text for explanations
(adapted from [32]).
Finally, both protons could be knocked out from the p-shell and would result in the 24 O
configuration of π(0p1/2,3/2 )−2 π(0d5/2 )2 . In this case very highly excited states in 24 O above the
one-proton separation energy are populated, which could decay to nitrogen isotopes but would
more likely result in neutrons emitted sequentially from an unbound continuum of states in 24 O,
23 O and even 22 O. These excitations and the subsequent emission of neutrons could explain the
non-resonant shape of the decay energy spectrum for 22 O. This is consistent with the observation
of only a non-resonant background in the spectrum of the decay of 22 O shown in the bottom
panel of Fig. 8.
The resonance at a decay energy of 45(2) keV in 23 O translates into an excitation energy of
2.79(13) MeV, given that the neutron separation energy is 2.74(13) MeV [33]. This assignment is
based on the assumption that the neutron decays to the ground state of 22 O. The decay to excited
states of 22 O is unlikely as was discussed in Ref. [13]. Recently, the observation of a 3/2+
state has been reported in the reaction 22 O(d, p) [10]. This reaction predominantly populates
particle states while the present knockout reaction populates hole states. The fact that the present
measurement does not populate the 3/2+ lends further support to the selectivity of the proposed
direct reaction mechanism. The observations of the two experiments are complementary and the
interpretation within the shell model has been presented in Ref. [13].
In addition to the two proton knockout (π(0p1/2,3/2 )1 , (0d5/2 )1 ), with subsequent emission
of a neutron, the 1/2+ ground state and the 5/2+ first excited state of 23 O can also be populated
directly by the three nucleon knockout of two protons and one neutron. The removal of two
π(0d5/2 ) protons together with a ν(1s1/2 ) or ν(0d5/2 ) neutron also populates the 1/2+ ground
state and the 5/2+ state first excited state of 23 O, respectively. These two different mechanisms
cannot be distinguished in the present experiment although this is of no consequence as they
populate the same final states in 23 O.
Fig. 11 summarizes the population of the three oxygen isotopes within the two-proton knockout reaction mechanism. The removal of the two d5/2 protons predominantly leads to the ground
state of 24 O, while the removal of one d5/2 and one p-shell proton leads to a continuum of highly
excited states in 24 O. These proton excitations can then mix with neutron excitations as shown in
Fig. 10 to populate discrete states in 23 O. The 5/2+ state is neutron unbound and decays to the
ground state of 23 O as indicated by the arrow in Fig. 11. 21 O can be populated by the sequential
emission of neutrons via continuum states in 23 O and 22 O.
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Fig. 11. Calculated proton (d5/2 )1 × (p1/2,3/2 )−1 cross-shell excitation strength function for two-proton removal
from 26 Ne [30,31] and the three lowest states in 22–24 O (dashed lines: calculations, solid lines: experiments, adapted
from [34]).
5. Conclusions
We have studied the two-proton removal reaction from 26 Ne populating several neutron-rich
oxygen isotopes. The data were interpreted with a reaction model that includes the knock out
of valence and core protons. The knock out of the valence protons is consistent with the nonobservation (or at most weak population) of excited states in 24 O. The knock-out of one valence
and one core proton leads to the selective population of the 5/2+ excited state in 23 O which we
observed at a resonance energy of 45(2) keV, corresponding to a neutron-unbound resonance in
23 O at 2.79(13) MeV.
Acknowledgements
We would like to thank the members of the MoNA Collaboration G. Christian, C. Hoffman,
K.L. Jones, K.W. Kemper, P.V. Pancella, G.F. Peaslee, W.F. Rogers, S.L. Tabor, and approximately 50 undergraduate students for their contributions to this work. We would like to thank
R.A. Kryger, C. Simenel, J.R. Terry, and K. Yoneda for their valuable help during the experiment.
Financial support from the National Science Foundation under grant Nos. PHY-0110253, PHY0354920, PHY-0555366, PHY-0555445, and PHY-0606007 is gratefully acknowledged. J.E.F.
and J.T. acknowledge support from the Research Excellence Fund of Michigan and from the
United Kingdom Science Technology Facilities Council (STFC) under Grant No. EP/D003628,
respectively.
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